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- W3137249543 abstract "The Laplacian matching polynomial of a graph G, denoted by (mathscr {LM}(G,x)), is a new graph polynomial whose all zeros are nonnegative real numbers. In this paper, we investigate the location of zeros of the Laplacian matching polynomials. Let G be a connected graph. We show that 0 is a zero of (mathscr {LM}(G, x)) if and only if G is a tree. We prove that the number of distinct positive zeros of (mathscr {LM}(G,x)) is at least equal to the length of the longest path in G. It is also established that the zeros of (mathscr {LM}(G,x)) and (mathscr {LM}(G-e,x)) interlace for each edge e of G. Using the path tree of G, we present a linear algebraic approach to investigate the largest zero of (mathscr {LM}(G,x)) and particularly to give tight upper and lower bounds on it." @default.
- W3137249543 created "2021-03-29" @default.
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- W3137249543 date "2022-04-11" @default.
- W3137249543 modified "2023-10-14" @default.
- W3137249543 title "On the location of zeros of the Laplacian matching polynomials of graphs" @default.
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- W3137249543 doi "https://doi.org/10.1007/s10801-022-01130-5" @default.
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